Numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "Elemag"
In the article the mathematical model and computer program for numerical modeling of plasma accumulation, heating and confinement processes in thermonuclear reactor "Elemag" is considered. In a basis of model the equations of material and power balance are fixed in view of specific feature...
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2003
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| Cite this: | Numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "Elemag" / O.A. Lavrent’ev, S.V. Germanova, B.A. Shevchuk // Вопросы атомной науки и техники. — 2003. — № 1. — С. 40-42. — Бібліогр.: 4 назв. — англ. |
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| author | Lavrent’ev, O.A. Germanova, S.V. Shevchuk, B.A. |
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| citation_txt | Numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "Elemag" / O.A. Lavrent’ev, S.V. Germanova, B.A. Shevchuk // Вопросы атомной науки и техники. — 2003. — № 1. — С. 40-42. — Бібліогр.: 4 назв. — англ. |
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| description | In the article the mathematical model and computer program for numerical modeling of plasma accumulation, heating and confinement processes in thermonuclear reactor "Elemag" is considered. In a basis of model the equations of material and power balance are fixed in view of specific features of multislit electromagnetic traps. The results of a starting mode reactor modeling, the stationary state execution, ways of capacity regulation, results of direct transformation of a-particles kinetic energy in electrical one are offered.
В роботі розглядається математична модель та комп’ютерна програма для чисельного моделювання накопичення нагріву та утримання плазми в термоядерному реакторі “Елемаг”. В основу програми покладено рівняння матеріального та енергетичного балансу з урахуванням специфічних особливостей багатощілинних електромагнітних пасток. Представлені результати моделювання стартового режиму, стаціонарного стану, методи регулювання потужності, результати прямого перетворення кінетичної енергії a-часток в електричну.
В работе рассматривается математическая модель и компьютерная программа для численного моделирования накопления, нагрева и удержания плазмы в термоядерном реакторе «Элемаг». В основу модели положены уравнения материального и энергетического баланса с учетом специфических особенностей многощелевых электромагнитных ловушек. Представлены результаты моделирования стартового режима, стационарного состояния, методы регулирования мощности, результаты прямого преобразования кинетической энергии a-частиц в электрическую.
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NUMERICAL MODELING OF PROCESSES OF PLASMA ACCUMULATION,
HEATING AND CONFINEMENT IN THERMONUCLEAR REACTOR
"ELEMAG" *
O.A.Lavrent’ev, S. V. Germanova, B. A. Shevchuk
Institute of Plasma Physics, National Scientific Center “Kharkov Institute of Physics and
Technology”, Kharkov, Ukraine, <lavr@ipp.kharkov.ua>, tel. 0572 35 64 38
In the article the mathematical model and computer program for numerical modeling of plasma accumulation, heating
and confinement processes in thermonuclear reactor "Elemag" is considered. In a basis of model the equations of
material and power balance are fixed in view of specific features of multislit electromagnetic traps. The results of a
starting mode reactor modeling, the stationary state execution, ways of capacity regulation, results of direct
transformation of α - particles kinetic energy in electrical one are offered.
* The research described in this publication was made possible in part by Grant #1341 from STCU
PACS: 52.55.-s, 52.50.Gj
MATHEMATICAL PROGRAM OF PLASMA
PROCESSES NUMERICAL MODELING IN
THERMONUCLEAR REACTOR
The equations describe dependence of complete
quantity electrons Ne, complete quantity of ions Ni,
complete power contents in an electrons component of
plasma We = 1.5TeNe and complete power contents in a
ion component of plasma Wi = 1.5TiNi from time of
plasma accumulation
dNe/dt = Ie/e + Г – Ie┴ -Ie 1 )׀׀ )
dNi/dt = Г – Ii - Iα (2)
dWe/dt = Peh - Pek (3)
dWi/dt = Pih - Pik (4)
Ie, - current of electrons injected in a trap. At an initial
stage of plasma accumulation it is limited by formation of
the virtual cathode at the center of a trap. The special
function, limiting a current of electron injection at
approximation of volumetric charge potential to potential
of the cathode, is entered at numerical modeling in the
program.
Г = <σeve>napNe (5)
quantity of electrons and ions pairs formed in plasma
volume in time unit (s) as a result of neutral gas
ionization, <σeve> - speed of ionization, nap - neutral gas
density in plasma. The neutral gas "burns out" and it
density in plasma is less than neutral gas density acting in
the vacuum chamber
nap = nam/(1 + <σeve>Ne/vaSp) (6)
where va = (8kTa/πma)1/2 - speed of neutral gas molecules,
Sp - area of plasma limiting surface.
Electrons are lost from a trap as a result of cross
transfer through a magnetic field with an exit on limiting
anode diaphragms and also as a result of longitudinal
diffusion in space of speeds with overcoming of an
electrostatic barrier Фe and exit on electrodes of
electrostatic magnetic slits lock-out system.
The cross diffusion flow in a multislit electromagnetic
trap with axisymmetric geometry of magnetic field in
view of electrons mobility in a strong electrical field was
calculated in works [1,2]
Ie┴ = N[Dea(1+Фp/2Te0) + Dei] ne0FR2 (7)
where N – quantity of magnetic slits in a trap, Dea = Te νea
/ me ωce
2 , Deі = Te νei / me ωce
2 - factors of electrons
diffusion on plasma neutral atoms and ions,
Фp - plasma potential (in power units), ne0, Te0 - plasma
density and electrons temperature in the central area of a
trap, F - factor which is taking into account magnetic field
geometry, R - radius of a trap on a ring magnetic slit.
Longitudinal losses according to [3] are determined by
speed of particle maxwellization in plasma. All particles
which have achieved energy of a potential barrier leave
plasma volume at small speed of maxwellization and
I 2)4 = ׀׀ π)1/2 e4 λn2 Vp m-1/2 T-3/2 exp-γ (8)
At the large speed of maxwellization the barrier exit of
particles is limited by throughput of magnetic slits
I 2 = ׀׀ (π)1/2crpnkT(B0/BA)1/2 exp-γ / eBAγ1/2 (9)
Vp - plasma volume, γ = Ф/T, rp - radius of plasma, BA -
magnetic field in a ring slit, B0 = B(rp(. We take the
smaller value from these two expressions for longitudinal
electron losses Ie׀׀ and longitudinal ion losses Ii.
"Depression" of volumetric charge potential ΔФ is
calculated with the help of the A. Kaye theory [4],
allowing to find electrons flow, circulating in a magnetic
slit
ΔФ = 4πсne0kTe(B0/BA)1/2a0/veBA (10)
2a0 - width of a magnetic slit limited by anode
diaphragms, ve - electron speed in a magnetic slit.
α - particles flow from plasma on the first wall of
thermonuclear reactor (in recalculation on singly ions)
Iα = 0.5<σfvi>ni
2Vp (11)
Capacity Pe = ФaIe is entered into plasma by electrons
injection. It is spent for creation of volumetric charge
electrical field, neutral atoms excitation and ionization,
electrons and ions heating, covering of energy losses
connected with a particles exit from a trap, recharging,
bremsstrahlung and betatron radiation. The additional
capacity connected with energy recuperation of
thermonuclear α-particles Pα = ФpIα and hot ions leaving
the trap through magnetic slits Pi = ФiIi overcoming a
potential barrier Фi will be entered through the electron
channel in process of plasma accumulation and heating.
Thus the following capacity is entered through the
electron channel in a trap
40 Problems of Atomic Science and Technology. 2003. № 1. Series: Plasma Physics (9(. P. 40-42
mailto:lavr@ipp.kharkov.ua
Peh = Pe + Pα + Pi (12)
Collisional and collisionless energy transfer from
electrons to ions is the source of energy for ions heating.
Energy, which is transferred by collisional way
Peq = 1.5(Te –Ti)Ne/τeq (13)
where τeq = 3miTe
3/2/8(2πme(1/2e4λne.
The collisionless energy transfer is carried out by ions
acceleration formed at neutral atoms ionization in an
electrical field of a volumetric charge. The efficiency of
heating depends on a place of neutral atom ionization on a
slope of a potential well, what, in turn, depends on a ratio
of neutral atom, λl penetration depth to depth of electrical
field λd penetration into plasma. Capacity, which is
transferred by collisionless way
PE = αФpГ (14)
where α=1/(1+λl/λd), λl=Va/<σeve>na, λd = (Фp/6πe2ne)1/2
Thus capacity of ions heating
Pih = Peq + PE (15)
The expense of capacity through the electrons channel
Pek = Pε + Peq + PE +Pe┴ + Pe|| + Pbr (16)
where: Pε = εГ - losses on neutral atoms excitation and
ionization, ε = 70 eV - the energy is spent on the
ionization act and accompanying excitation of neutral gas
atoms, Peq and PE - capacity on collisional and collisionles
ions heating, Pe┴ = 1.3TeIe┴, Pe║ = ФaIe║ - losses
connected with electrons transfer across a magnetic field
on anode diaphragms and along a magnetic field on
electrostatic system electrodes, Pbr - losses on
bremsstrahlung. The losses on betatron radiation are not
taken into account, as the plasma in basic volume is
outside of a magnetic field.
The expense of capacity through ions channel
Pik = Pi _+Pp +Pr (17)
where: Pi = ФiIi - losses connected with ions exit, Pp =
1.5TiIα - losses connected to ions removal from plasma in
result of thermonuclear reaction, Pr = Ti<σ10vi>napvi –
losses on recharge.
STARTING MODE MODELING
Thermonuclear reactor «Elemag» represents a multislit
electromagnetic trap with axisymmetric magnetic field
geometry. Quantity of magnetic slits is N = 40. Radius on
a ring magnetic slit 3.6 m, length between axial apertures
- 90 m. Width of a magnetic slit limited by anode
diaphragms is 2а0 = 0.5 cm. Plasma volume - 1140 m3,
area of a surface limiting plasma - 1140 m2. A magnetic
field in a ring magnetic slit – ВA = 70 kGs, in axial
apertures ВA0 = 140 kGs. Electrostatic potential closing
magnetic slits -700 kV.
The modeling of plasma accumulation and heating in a
starting mode was carried out in real time. Plasma density
ne,i electrons and ions temperature Te and Ti, plasma
potential Фp and potential "depression" in a magnetic slit ∆
Ф, neutral gas density in plasma nap, current of electrons
injection Ie, current of cross Ie⊥ and longitudinal Ie║ electrons
transfer, current of ions in magnetic slits Ii, current of α-
particles Iα and capacities which are entered in reactor and
spent there were display on the screen of the monitor. The
results of modeling are submitted in the figure.
Plasma parameters achievable in a starting mode depend
on capacity of electron injection, and the growth rate is
determined by quantity of entered neutral gas. Electrons
temperature is less than ions temperature, which is
connected with proceeding plasma accumulation and
expense of electrons channel energy on entered neutral
gas ionization and heating. Besides the electrons channel
spends energy for bremsstrahlung and indemnification of
electrons losses on cross and longitudinal transfer.
STATIONARY MODE
In a starting mode the achievement of calculated plasma
parameters does not stop further plasma accumulation and
heating process. The stationary mode is achieved when the
conditions of material and power balance will be executed.
Accumulated plasma density is regulated by neutral gas
submission. In a stationary mode the quantity of gas, acting
in plasma, Г should correspond to quantity of substance
leaving a trap α-particles and ions of deuterium and tritium I
α + Ii. Plasma density will remain constant during all
operating time of thermonuclear reactor at performance of
neutral gas balance Г = Iα + Ii, see figure, point “a”. Increase
of gas submission, Г> Iα + Ii or reduction of gas submission
Г < Iα + Ii leads to plasma density increase or reduction with
exit on a new stationary level Г = Iα + Ii. Other plasma
parameters are arranged under a new stationary condition.
41
Fig.
The mechanism of thermonuclear reaction α-particles
energy recuperation and connected with it energy recuperation
of fast electrons in an external electrical field is included with
growth of density and temperature of plasma ions. When the
capacity of recuperated energy Pe║ becomes equal to capacity
of electron injection Pe, feeding of electrons injectors can be
switched to a source of recuperated energy. At the further
increase of plasma parameters the external electron injection is
switched off and work of reactor proceeds in an independent
mode. Thermonuclear fuel (as equal component of a mix
deuterium and tritium) is entered in plasma, there is an
ionization of neutral gas, having heated electrons and ions in a
potential well volumetric charge, thermonuclear reaction
between ions, energy recuperation α-particles and energy
recuperation fast electrons, restoring power balance, see
figure, point “b”. The de-energizing of electrons injection does
not render essential influence on process of plasma
accumulation, the accumulation proceeds for the account of α-
particles energy recuperation. The adjustment of ions
temperature is achieved by change of factor of collisionless
energy transfer from electrons to ions, α. At reduction of
neutral gas temperature up to temperature of liquid nitrogen α
is increased in (300/77.2)1/2 times, see figure, the point "с".
The ion temperature is grows, electron temperature,
accordingly, falls.
Complete thermal capacity of thermonuclear reactor Pf = 4.
01 GWt, capacity of α- particles recuperated energy, Pα = 192
MWt, PE = 127 MWt is allocated directly as electrical
capacity (in a high-voltage electrical circuit). Pα - PE = 65
MWt - internal energy expense in thermonuclear reactor on
ionization and heating of entered fuel and covering of power
losses from plasma. A complete flow of thermonuclear
neutrons from plasma Nn = 1.43*1021 n/s, density of neutrons
flow on the first wall nn = 1.24*1014 n/cm2s. The expense of
thermonuclear fuel (equal component of gases deuterium and
tritium mix) mD,T = 1.22*10-2 g/s.
REGULATION OF THERMONUCLEAR
REACTOR CAPACITY
The most simple and convenient way of capacity
adjustment consists in regulation of fuel submission into
reactor as well as in any electrical generator working on liquid
or gaseous fuel. The complete stop of reactor occurs in time t
≈5s at the de-energizing of fuel supply (Г = 0).
From other possible ways of thermonuclear reactor
capacity adjustment it is possible to apply change of a
magnetic field BA or change of electrostatic potential ФA.
In the first case energy losses on the cross electrons
transfer increase with appropriate decrease of plasma
temperature and density. In the second case electrostatic
barriers Фe and Фi decrease with the appropriate increase of
particles and energy losses on diffusion in space of speeds.
These ways of capacity adjustment are inertialless and should
be applied to fast changes of thermonuclear reactor capacity or
its stop in an emergency.
CONCLUSION
The main result of work is plasma parameters theoretical
account and modeling in thermonuclear reactor «Elemag».
Reactor comes on calculated plasma parameters for t ≈ 30 sec
in a starting mode at a current of electrons injection 100 A and
consumption of the equal component of gases deuterium and
tritium mix 4.63*10-2 g/s. Energy recuperation of
thermonuclear α-particles in an electrical field of electron
volumetric charge with subsequent energy recuperation of
electrons in an external electrical field allows to disconnect
electron injection. The stationary condition with plasma
parameters ne,i = 8*1013 cm-3, Те = 33.9 keV, Тi = 38.7 keV is
achieved by reduction of neutral gas submission up to
1.21*10-2 g/s. The complete thermal capacity of thermonuclear
reactor Pf = 4.01 GWt, Pnet = 127 MWt transforms directly in
electrical energy (electrical current of a high voltage). Plasma
parameters of a stationary mode are confirmed by theoretical
accounts of the thermonuclear reactor basic characteristics.
REFERENCES
1. S.V. Germanova, O.A. Lavrent’ev, V.I. Petrenko.
Crossfield transport of electrons in a multislit
electromagnetic trap with axisymmetric magnetic
field// Voprosy Atomnoj Nauki I Tekhniki.Ser:
Termoyadernyi Sintez /Moscow, 3, 1988, pp. 69 - 72.
2. S.V.Germanova, O.A. Lavrent’ev, V.I. Petrenko.
Crossfield transport of electrons in a multislit
electromagnetic trap across the end magnetic
surfaces// Voprosy Atomnoj Nauki I Tekhniki. Ser:
Termoyadernyi Sintez/ Moscow, 2, 1991, pp. 74 - 76.
3. E. E. Jushmanov. Charge particles injection in
magneto-electrostatic trap.// Fizika plazmy.
4,1978,p.32.
4. A.S. Kaye.Adiabatic cusp losses/ CLM, 1969,p. 193.
ЧИСЕЛЬНЕ МОДЕЛЮВАННЯ НАКОПИЧЕННЯ НАГРІВУ ТА УТРИМАННЯ ПЛАЗМИ В
ТЕРМОЯДЕРНОМУ РЕАКТОРІ “ЕЛЕМАГ”
О. О. Лаврентьєв
В роботі розглядається математична модель та комп’ютерна програма для чисельного моделювання
накопичення нагріву та утримання плазми в термоядерному реакторі “Елемаг”. В основу програми покладено
рівняння матеріального та енергетичного балансу з урахуванням специфічних особливостей багатощілинних
електромагнітних пасток. Представлені результати моделювання стартового режиму, стаціонарного стану,
методи регулювання потужності, результати прямого перетворення кінетичної енергії α-часток в електричну.
ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ НАКОПЛЕНИЯ, НАГРЕВА И УДЕРЖАНИЯ ПЛАЗМЫ В
ТЕРМОЯДЕРНОМ РЕАКТОРЕ «ЭЛЕМАГ»
О. А. Лаврентьев
В работе рассматривается математическая модель и компьютерная программа для численного моделирования
накопления, нагрева и удержания плазмы в термоядерном реакторе «Элемаг». В основу модели положены уравнения
материального и энергетического баланса с учетом специфических особенностей многощелевых электромагнитных
42
ловушек. Представлены результаты моделирования стартового режима, стационарного состояния, методы
регулирования мощности, результаты прямого преобразования кинетической энергии α-частиц в электрическую.
43
Stationary mode
Conclusion
References
Чисельне моделювання накопичення нагріву та утримання плазми в термоядерному реакторі “Елемаг”
О. О. Лаврентьєв
В роботі розглядається математична модель та комп’ютерна програма для чисельного моделювання накопичення нагріву та утримання плазми в термоядерному реакторі “Елемаг”. В основу програми покладено рівняння матеріального та енергетичного балансу з урахуванням специфічних особливостей багатощілинних електромагнітних пасток. Представлені результати моделювання стартового режиму, стаціонарного стану, методи регулювання потужності, результати прямого перетворення кінетичної енергії -часток в електричну.
О. А. Лаврентьев
|
| id | nasplib_isofts_kiev_ua-123456789-110340 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-01T15:19:49Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Lavrent’ev, O.A. Germanova, S.V. Shevchuk, B.A. 2017-01-03T15:22:00Z 2017-01-03T15:22:00Z 2003 Numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "Elemag" / O.A. Lavrent’ev, S.V. Germanova, B.A. Shevchuk // Вопросы атомной науки и техники. — 2003. — № 1. — С. 40-42. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 52.55.-s, 52.50.Gj https://nasplib.isofts.kiev.ua/handle/123456789/110340 In the article the mathematical model and computer program for numerical modeling of plasma accumulation, heating and confinement processes in thermonuclear reactor "Elemag" is considered. In a basis of model the equations of material and power balance are fixed in view of specific features of multislit electromagnetic traps. The results of a starting mode reactor modeling, the stationary state execution, ways of capacity regulation, results of direct transformation of a-particles kinetic energy in electrical one are offered. В роботі розглядається математична модель та комп’ютерна програма для чисельного моделювання накопичення нагріву та утримання плазми в термоядерному реакторі “Елемаг”. В основу програми покладено рівняння матеріального та енергетичного балансу з урахуванням специфічних особливостей багатощілинних електромагнітних пасток. Представлені результати моделювання стартового режиму, стаціонарного стану, методи регулювання потужності, результати прямого перетворення кінетичної енергії a-часток в електричну. В работе рассматривается математическая модель и компьютерная программа для численного моделирования накопления, нагрева и удержания плазмы в термоядерном реакторе «Элемаг». В основу модели положены уравнения материального и энергетического баланса с учетом специфических особенностей многощелевых электромагнитных ловушек. Представлены результаты моделирования стартового режима, стационарного состояния, методы регулирования мощности, результаты прямого преобразования кинетической энергии a-частиц в электрическую. The research described in this publication was made possible in part by Grant #1341 from STCU. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "Elemag" Чисельне моделювання накопичення нагріву та утримання плазми в термоядерному реакторі “Елемаг” Численное моделирование накопления, нагрева и удержания плазмы в термоядерном реакторе «Элемаг» Article published earlier |
| spellingShingle | Numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "Elemag" Lavrent’ev, O.A. Germanova, S.V. Shevchuk, B.A. Magnetic confinement |
| title | Numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "Elemag" |
| title_alt | Чисельне моделювання накопичення нагріву та утримання плазми в термоядерному реакторі “Елемаг” Численное моделирование накопления, нагрева и удержания плазмы в термоядерном реакторе «Элемаг» |
| title_full | Numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "Elemag" |
| title_fullStr | Numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "Elemag" |
| title_full_unstemmed | Numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "Elemag" |
| title_short | Numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "Elemag" |
| title_sort | numerical modeling of processes of plasma accumulation, heating and confinement in thermonuclear reactor "elemag" |
| topic | Magnetic confinement |
| topic_facet | Magnetic confinement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110340 |
| work_keys_str_mv | AT lavrentevoa numericalmodelingofprocessesofplasmaaccumulationheatingandconfinementinthermonuclearreactorelemag AT germanovasv numericalmodelingofprocessesofplasmaaccumulationheatingandconfinementinthermonuclearreactorelemag AT shevchukba numericalmodelingofprocessesofplasmaaccumulationheatingandconfinementinthermonuclearreactorelemag AT lavrentevoa čiselʹnemodelûvannânakopičennânagrívutautrimannâplazmivtermoâdernomureaktoríelemag AT germanovasv čiselʹnemodelûvannânakopičennânagrívutautrimannâplazmivtermoâdernomureaktoríelemag AT shevchukba čiselʹnemodelûvannânakopičennânagrívutautrimannâplazmivtermoâdernomureaktoríelemag AT lavrentevoa čislennoemodelirovanienakopleniânagrevaiuderžaniâplazmyvtermoâdernomreaktoreélemag AT germanovasv čislennoemodelirovanienakopleniânagrevaiuderžaniâplazmyvtermoâdernomreaktoreélemag AT shevchukba čislennoemodelirovanienakopleniânagrevaiuderžaniâplazmyvtermoâdernomreaktoreélemag |